幂次wendroff型积分不等式及其在分数阶偏微分方程中的应用

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals Pub Date : 2025-02-19 DOI:10.1016/j.chaos.2025.116129

Yanlin Yang, Baishun Wang, Jun Zhou

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引用次数: 0

摘要

本文推广了一类具有两个变量的幂次Gronwall不等式，即幂次Wendroff不等式。得到了其解的递归估计和有界性。进一步证明了该不等式可用于研究Caputo分数阶偏微分方程的边值问题，如解的唯一性、有界性和连续依赖性。最后，我们给出了两个具体的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Powered Wendroff-type integral inequality and application to fractional PDEs

In this paper, we generalize a powered Gronwall inequality with two variables, i.e. so-called powered Wendroff inequality. We get the recursive estimate and boundedness of its solutions. Further, we exhibit that our inequality can be used to study the boundary value problems of Caputo fractional PDEs, such as uniqueness, boundedness and continuous dependence of solutions. Finally, we give two concrete examples.

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来源期刊

Chaos Solitons & Fractals 物理-数学跨学科应用

CiteScore

13.20

自引率

10.30%

发文量

1087

审稿时长

9 months

期刊介绍： Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.